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Ierofanga [76]
3 years ago
8

explain how the following ordered pairs represent or doesn’t represent a function - {(-3,5), (-2,5), (-1,5), (0,5), (1,5), (2,5)

Mathematics
1 answer:
Luden [163]3 years ago
4 0
This represents a function because there are different inputs for each output. Different x values for the y values.
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What does this mean!
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8 0
3 years ago
one leg of a right triangle is 5 millimeters shorter than the longer leg and the hypotneuse is 5 millimeters longer than the lon
Makovka662 [10]
The answer, in short, is that the short leg equals 15 mm, the long leg equals 20 mm, and the hypotenuse equals 25mm. but if you'd like to see how I solved it, here are the steps.
-----------------------------
The Pythagorean theorem (also known as Pythagoras's Theorem) can be used to solve this. This theorem states that one leg or a right triangle squared plus the other side of that same triangle squared equals the hypotenuse of that triangle squared. To put it in equation form, L² + L² = H².

Let's call the longer leg B, the shorter leg A, and the hypotenuse H.
From the question, we know that A = B - 5, and H = B + 5. 

So if we put those values into an equation, we have (B - 5)² + B² = (B + 5)²

Now, to solve. Let's square the two terms in parentheses first:
(B² - 5B - 5B + 25) + B² = B² + 5B + 5B + 25

Now combine like terms:
2B² -10B + 25 = B² + 10B + 25

And now we simplify. Subtract 25 from each side:
2B² - 10B = B² + 10B

Subtract B² from each side:
B² - 10B = 10B

Add 10B to each side:
B² = 20B

And finally, divide each side by B:
B = 20

So that's the length of B. Now to find out A and H.
A = B - 5, so A = 15.
H = B + 5, so H = 25.

And your final answer is A = 15mm, B = 20mm, and H = 25mm
7 0
3 years ago
If 2y=x³ + 2x², find dy/dx when x=2.
scZoUnD [109]

Answer:

10

Step-by-step explanation:

\boxed{\textsf{If }y=x^n,\: \textsf{then }\dfrac{\text{d}y}{\text{d}x}=nx^{n-1}}

<u>Given equation</u>:

2y=x^3+2x^2

Isolate y by dividing both sides by 2:

\implies y=\dfrac{1}{2}x^3+x^2

Differentiate with respect to x:

\implies \dfrac{\text{d}y}{\text{d}x}=3 \cdot \dfrac{1}{2}x^{3-1}+2 \cdot x^{2-1}

\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{3}{2}x^2+2x

Finally, substitute x = 2 into the differentiated equation:

\begin{aligned} \implies \dfrac{\text{d}y}{\text{d}x} & =\dfrac{3}{2}(2)^2+2(2)\\\\ & = \dfrac{3}{2}(4)+4\\\\ & = \dfrac{12}{2}+4\\\\ & = 6+4\\\\ & = 10\end{aligned}

Learn more about differentiation here:

brainly.com/question/27958412

brainly.com/question/26488862

5 0
2 years ago
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